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If x & y are integers and y=|x+3| + |4-x|, does y equals 7?
1) x < 4
2) x > -3
Had a hard time solving this, would like to know how to solve this using number picking approach as well as algebraic approach. Thanks.
OA is
Guys, the be low is my approcah for any modulus qtn in GMAT.
Remember.
The meaning of |x-y| is "On the number line, the distance of X from +Y"
The meaning of |x+y| is "On the number line, the distance of X from -Y"
The meaning of |x| is "On the number line, the distance of X from 0".
Qtn:
for integers X and Y, If y=|x+3| + |4-x|, does y equals 7
==> is the SUM of the distance b/e x and -3 , and x and 4 equals to 7?
==> .........-3......0...........4..... observe that X has to be anywhere b/w -3 and 4 or on any of these points for the total distance to be 7
Stmnt1: X < 4: Answer could be Yes if X is < 4 and b/w -3 and 4 but from the given information (i.e X<4) X could be some where left to -3 in which case the total distance would be > 7 hence insufficient.
......X....-3......0..........4 answer to the qtn: NO
or ............-3...X...0.........4 answer to the qtn: YES
Stmnt2: X > -3: Answer could be Yes if X is > -3 and b/w -3 and 4 but from the given information (i.e X>-3) X could be some where right to 4 in which case the total distance would be > 7 hence insufficient.
..........-3......0..........4...X... answer to the qtn: NO
or ..........-3...X...0.........4 answer to the qtn: YES
1&2
X must be b/w -3 and 4
..........-3.X.X.X...0.X.X.X.X.X...4...... answer is always YES..hence Sufficient.
Answer C.
Hope it helps